Related Experiment Video
Updated: May 1, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
709
Finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems.
Kazutaka Kanno1, Atsushi Uchida1
1Department of Information and Computer Sciences, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama City, Saitama, 338-8570, Japan.
Summary
We developed a new method to calculate Lyapunov exponents in complex systems with time delays. Increasing calculation time or delay time reduces the variability of these exponents, following a power-law relationship.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Time-Delayed Systems
Background:
- Lyapunov exponents quantify the rate of divergence of nearby trajectories in dynamical systems.
- Calculating Lyapunov exponents in systems with time delays presents significant challenges.
- Understanding the stability and predictability of time-delayed nonlinear systems is crucial.
Purpose of the Study:
- To introduce a novel computational method for finite-time Lyapunov exponents (FTLEs) in time-delayed nonlinear dynamical systems.
- To analyze the statistical properties of FTLEs in the Mackey-Glass model with time-delayed feedback.
- To investigate the impact of finite time and delay time on the variability of FTLEs.
Main Methods:
- Development of a new algorithm for calculating FTLEs in nonlinear systems with time delays.
- Application of the method to the well-established Mackey-Glass model.
- Statistical analysis of the probability distribution of FTLEs and the FTLE spectrum.
Main Results:
- The standard deviation of the FTLE probability distribution exhibits power-law scaling with an exponent of approximately 0.5 as finite time or delay time increases.
- This power-law behavior was also observed in the finite-time Lyapunov spectrum.
- The findings indicate a predictable reduction in the variability of Lyapunov exponents with increased temporal scales.
Conclusions:
- The proposed method provides an effective tool for analyzing the dynamics of time-delayed systems.
- The observed power-law scaling suggests underlying universal properties in the statistical behavior of FTLEs in such systems.
- This research contributes to a better understanding of chaos and predictability in complex, time-delayed phenomena.
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